System and method for geo-registration with global positioning and inertial navigation

ABSTRACT

A position estimation system including a first arrangement for providing an image with a known target in a known reference frame. A second arrangement correlates the image with a stored image. The correlation is used to compute an error with respect to a position estimate. In a specific embodiment, the error is referenced with respect to first (x), second (y) and third (z) directions. A target location error is computed with respect to a stored image provided by a target image catalog. The target image catalog includes target geo-locations and digital terrain elevation data. In an illustrative application, the image data is provided by synthetic aperture radar and forward-looking infrared systems. An observation model and a measure noise matrix are Kalman filtered to ascertain a position error in navigation data generated by an integrated inertial navigation and Global Positioning system.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to inertial navigation and globalposition. More specifically, the present invention relates to systemsand methods for improving the GPS counter-jamming performance ofinertial navigation systems.

2. Description of the Related Art

Inertial navigation systems typically use gyroscopes and accelerometersto provide precision vehicular navigation. Unfortunately, inertialnavigation accuracy degrades because of instrument calibration errorsand other errors. These navigation errors typically grow as a functionof time. Independent observations of the vehicle navigation informationare needed to bind these navigation errors. Therefore, sensors, otherthan INS, are needed in order to obtain independent navigationinformation. Hence, a conventional approach for correcting these errorsinvolves the integration of a Global Position System (GPS) receiver withthe inertial navigation system. However, the GPS is vulnerable tojamming which can impede the ability of the GPS system to correct theinertial navigation errors.

Typically, to counter the effects of GPS jamming, designers haveendeavored to: 1) improve the accuracy of the inertial navigation systemand 2) make the GPS receiver resistant to jamming. However, theseapproaches are expensive and limited in efficacy.

Hence, a need remains in the art for an effective yet inexpensive systemor method for improving the navigation accuracy of integrated inertialnavigation and Global Positioning Systems.

SUMMARY OF THE INVENTION

The need in the art is addressed by the position estimation system ofthe present invention. In a most general implementation, the inventivesystem includes a first arrangement for providing an image including aknown target in a known reference frame. A second arrangement correlatesthe image with a stored image. The correlation is used to compute anerror with respect to a position estimate.

In a specific embodiment, the error is referenced with respect to first(x), second (y) and third (z) directions. A target location error iscomputed with respect to a stored image provided by a target imagecatalog. The target image catalog includes target geo-locations anddigital terrain elevation data. In an illustrative application, theimage data is provided by synthetic aperture radar or forward-lookinginfrared systems. An observation model and a measure noise matrix areKalman filtered to ascertain a position error in navigation datagenerated by an integrated inertial navigation and Global Positioningsystem.

In the illustrative application, geo-registered SAR/FLIR imagery is usedto track targets and to determine a target location error (TLE). ThisTLE information is a set of error equations that describe therelationship between vehicle navigation information and target data. Inaccordance with the invention, this relationship is used to form anobservation model for vehicle navigation with respect to targetlocations. Using Kalman filtering and the observation model, vehiclenavigation errors can be bound and the navigation accuracy of thevehicle can be improved.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an illustrative implementation of aposition estimation system in accordance with the present teachings.

FIG. 2 is a simplified flow diagram showing an illustrativeimplementation of a position estimation method in accordance with thepresent teachings.

FIG. 3 is a diagram showing a geo-sighting error model in threedimensions in accordance with an illustrative application of the presentteachings.

DESCRIPTION OF THE INVENTION

Illustrative embodiments and exemplary applications will now bedescribed with reference to the accompanying drawings to disclose theadvantageous teachings of the present invention.

While the present invention is described herein with reference toillustrative embodiments for particular applications, it should beunderstood that the invention is not limited thereto. Those havingordinary skill in the art and access to the teachings provided hereinwill recognize additional modifications, applications, and embodimentswithin the scope thereof and additional fields in which the presentinvention would be of significant utility.

In general, in accordance with the present teachings, geo-registeredSAR/FLIR imagery is used to track targets and to determine a targetlocation error (TLE). The TLE is generated by a set of error equationsthat describe the relationship between the vehicle (sensor) navigationinformation and the target location. The geo-registered images obtainedfrom SAR/FLIR systems provide position estimates for a known pixel onthe ground or other reference frame through target recognition methods.This position estimate serves as an independent observation to binderrors in an inertial navigation system.

U.S. Pat. No. 5,485,384 entitled ON-BOARD NAVIGATION SYSTEM FOR ANAERIAL CRAFT INCLUDING A SYNTHETIC APERTURE SIDEWAYS LOOKING RADARissued Jan. 16, 1996 to B. Falconnet (hereinafter the “Falconnet”patent) the teachings of which are hereby incorporated herein byreference appears to teach the use of SAR (Synthetic Aperture Radar)sensors to obtain target imagery in the x and y horizontal plane. (Seealso U.S. Pat. No. 5,432,520 issued Jul. 11, 1995 to Schneider et al.and entitled SAR/GPS INERTIAL METHOD OF RANGE MEASUREMENT, the teachingsof which are herby incorporated herein by reference.) This imagery isthen correlated with maps of the geo-locations that are pre-stored inthe database to obtain two error equations in the x and y directions.These two error equations serve as an observation model for the Kalmanfilter to bind the vehicle navigation errors.

In accordance with the present invention, Falconnet's teachings areextended by: 1) including a third dimensional axis, the altitude of atarget image location and 2) providing a specific teaching as to how thethird dimension can be used to improve the navigational accuracy of anintegrated INS/GPS navigation system. The geo-registered imagery isextended to sensors from SAR or FLIR (forward-looking infrared) systems.A simple first order error model in the computed target geo-location isused to illustrate the effectiveness of Kalman filter updating usinggeo-registration imagery. Detailed x, y, and z observation equations areprovided which involve the vehicle's position, velocity, and attitude,as well as the angle between the horizontal plane and the slant plane.The position error differences can be minimized through optimalestimation techniques, such as Kalman filter, to bind INS navigationerrors. The equations form an observation matrix in a Kalman filter.

The method described in this invention can also be extended to anysensor on the vehicle that produces target location errors (TLE) on theknown target image because the TLE equations can be reduced to a set ofequations related to the-vehicle navigation errors and target imageposition errors.

FIG. 1 is a block diagram of an illustrative implementation of aposition estimation system in accordance with the present teachings. Theinventive system 10 includes an antenna array 12 which feeds a syntheticaperture radar (SAR) sensor 14. The sensor 14 is also adapted to processFLIR images. In accordance with the present teachings, the imagesprovided by the SAR/FLIR sensor 14 are input to an image processor 16.The image processor 16 uses data from a catalog of geo-registeredfeatures 18 to identify a target in a known reference frame as discussedmore fully below. Those skilled in the art will appreciate that theknown reference frame may be a surface other than the surface of theearth without departing from the scope of the present invention. Theoutput of the image processor 16 is input to an INS/GPS integrator 20.The integrator 20 includes an INS processor 22, a GPS processor 26 and aKalman filter 28. The INS processor 22 receives vehicle motion data froman on-board inertial measurement unit 24. The GPS processor 26 receivesa GPS signal along with noise and, in some environments, a GPS jammingsignal from a GPS receiver 25. The integrator 20 outputs vehicleposition, velocity, and attitude errors to a guidance processor 30. Theguidance processor 30 outputs vehicle position, velocity and attitudeinformation, corrected in accordance with the present teachings, for usein a conventional manner. The guidance processor 30 also feeds position,velocity, and velocity errors and range from the sensor to the target,back to the SAR/FLIR sensor 14 for generating TLE equations.

FIG. 2 is a simplified flow diagram showing an illustrativeimplementation of a position estimation method in accordance with thepresent teachings. In the best mode, the method 100 is implemented insoftware by the image processor 16 of FIG. 1. As illustrated in FIG. 2,the method 100 includes the step 102 of providing a GPS signal from theGPS receiver 25 via the GPS processor 26 (FIG. 1) and the step 104 ofproviding vehicle position, velocity, attitude and errors from the IMU24 via the INS processor 22 (FIG. 1). This data is analyzed by jamminglogic at step 106 to ascertain whether a jamming signal ‘J’ is presentand whether the jamming signal J exceeds a threshold ‘T’.

If J<T, then the data from the INS and GPS processors 22 and 26 is inputto the Kalman filter 28 (FIG. 1) directly at step 116.

If, however, J≧T, then at step 108 the system 10 generates targetlocation error (TLE) equations drawing data from the catalog ofgeo-registered features 18 (FIG. 1) at step 110. Next, at step 112, thecoordinates generated at step 108 are transformed. At step 114, anobservation matrix (H) and a measurement noise matrix (R) are generated.At step 116, this data is passed to the Kalman filter to bind thenavigation error as discussed above. At step 118, the output of theKalman filtering step 116 is used in a guidance process in aconventional manner.

Returning to FIG. 1, the catalog 18 is defined as the image and locationof each target image. This catalog details geo-locations and DTED(Digital Terrain Elevation Data). Based on the vehicle trajectorysupplied by the INS/GPS process, the image processor 16 determines whichgeo-target in the catalog 18 needs to be sighted. The processor 16 thensends this information to the SAR/FLIR sensor 14 to locate and then toexecute the geo-registered imagery. The SAR/FLIR sensor 14 determinesthe location of the geo target and correlates this imagery with theinformation in the catalog to determine the accuracy of the observation.

Errors in computed target geo-location can be primarily attributed tothree major sources: sensor position errors, sensor bearing errors andDTED errors. In accordance with the present teachings, these errors aretreated as being statistically independent and zero mean Gaussian. Forthe sake of simplicity, all other errors are assumed to be relativelysmall and are ignored. It is also assumed that the image of the targetcan be acquired. The DTED noise is treated herein as part of themeasurement noise in the z-direction of an ECEF (Earth Center EarthFixed) coordinate frame.

Errors in the sensor are directly transformed into the slant coordinateframe and then transformed to the platform coordinate frame. The slantcoordinate frame is defined as follows: x_(s) is along the vehiclevelocity axis {right arrow over (V)}, the z_(s) is perpendicular to theslant plane which is the plane that passes through {right arrow over(V)}_(D) and {right arrow over (R)}, and y_(s) forms a right-handcoordinate system.

Therefore, errors due to the sensor position errors in the slantcoordinate frame are derived as follows:

$\begin{matrix}{{{dx}_{s} = {{\Delta\;{\overset{\rightarrow}{r} \cdot \frac{\overset{\rightarrow}{v}}{v}}} + {\Delta\;{\overset{\rightarrow}{r} \cdot \overset{\rightarrow}{R} \cdot \cos}\;\phi}}}{{dy}_{s} = {\Delta\;{\overset{\rightarrow}{r} \cdot \overset{\rightarrow}{R} \cdot \sin}\;\phi}}{{dz}_{s} = {\Delta\;{\overset{\rightarrow}{r} \cdot \frac{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}{{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}}}}}} & \lbrack 1\rbrack\end{matrix}$where Δ{right arrow over (r)} and Δ{right arrow over (V)} are thevectors of the vehicle navigation position and velocity errors,respectively, in the body coordinate frame. {right arrow over (V)} isthe velocity vector of the vehicle, {right arrow over (R)} is the rangevector from the vehicle position to the known geo-location, and φ is theangle between the vehicle flight path and line of sight between vehicleand the target image.

The errors due to sensor bearing errors, in the slant coordinate frame,are derived as follows:

$\begin{matrix}{{{dx}_{s} = {{\frac{\Delta\;\overset{\rightarrow}{V}}{V} \cdot \frac{\;\overset{\rightarrow}{V}}{V}} + {{\frac{\Delta\;\overset{\rightarrow}{V}}{V} \cdot \overset{\rightarrow}{R} \cdot \cos}\;\phi}}}{{dy}_{s} = {{\frac{\Delta\;\overset{\rightarrow}{V}}{V} \cdot \overset{\rightarrow}{R} \cdot \sin}\;\phi}}{{dz}_{s} = {\frac{\Delta\;\overset{\rightarrow}{V}}{V} \cdot \frac{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}{{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}}}}} & \lbrack 2\rbrack\end{matrix}$

Next, we combine the errors provided by equations [1] and [2] to obtainthe following errors dx_(s), dy_(s), and dz_(s) that are in the slantcoordinate frame.

$\begin{matrix}{{{dx}_{s} = {\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \left( {\frac{\overset{\rightarrow}{V}}{V} + {{\overset{\rightarrow}{R} \cdot \cos}\;\phi}} \right)}}{{dy}_{s} = {{\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \overset{\rightarrow}{R} \cdot \sin}\;\phi}}{{dz}_{s} = {\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \frac{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}{{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}}}}} & \lbrack 3\rbrack\end{matrix}$Next, converting these errors, dx_(s), dy_(s), and dz_(s) into theplatform coordinate frame by the angle ψ (see FIG. 3).

FIG. 3 is a diagram showing a geo-sighting error model in threedimensions in accordance with an illustrative application of the presentteachings. The platform coordinate frame (vehicle body coordinate frame)is defined as follows: x_(p) is vehicle velocity direction, y_(p) is thevehicle right wing, and z_(p) forms a right hand coordinate system. Therelationship between the slant coordinate frame and the platformcoordinate frame is as follows:

$\begin{matrix}{\begin{pmatrix}{dx}_{p} \\{dy}_{p} \\{dz}_{p}\end{pmatrix} = {\begin{pmatrix}1 & 0 & 0 \\0 & {\cos\;\psi} & {{- \sin}\;\psi} \\0 & {\sin\;\psi} & {\cos\;\psi}\end{pmatrix}\begin{pmatrix}{dx}_{s} \\{dy}_{s} \\{dz}_{s}\end{pmatrix}}} & \lbrack 4\rbrack\end{matrix}$Inserting equation [3] into equation [4]:

$\begin{matrix}{{{dx}_{p} = {\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \left( {\frac{\overset{\rightarrow}{V}}{V} + {{\overset{\rightarrow}{R} \cdot \cos}\;\phi}} \right)}}{{dy}_{p} = {{{\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \overset{\rightarrow}{R} \cdot \sin}\;{\phi \cdot \cos}\;\psi} - {{\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \frac{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}{{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}} \cdot \sin}\;\psi}}}{{dz}_{p} = {{{\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \overset{\rightarrow}{R} \cdot \sin}\;{\phi \cdot \sin}\;\psi} + {{\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \frac{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}{{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}}}\cos\;\psi}}}} & \lbrack 5\rbrack\end{matrix}$where:

$\begin{matrix}{\psi = {{\tan^{- 1}\frac{R_{z}}{\sqrt{R_{x}^{2} + R_{y}^{2}}}\mspace{14mu}{and}\mspace{14mu}\overset{\rightarrow}{R}} = {\left( {R_{x},R_{y},R_{z}} \right).}}} & \lbrack 6\rbrack\end{matrix}$The classical Kalman filter is described as follows:{right arrow over (x)} _(k)=Φ_(k-1) {right arrow over (x)} _(k-1)+{right arrow over (w)} _(k-1) , {right arrow over (w)} _(k) ˜N({rightarrow over (0)},Q _(k)){right arrow over (z)} _(k) =H _(k) {right arrow over (x)} _(k) +{rightarrow over (v)} _(k) , {right arrow over (v)} _(k) ˜N({right arrow over(0)},R _(k))E[{right arrow over (x)}(0)]={right arrow over (x)} ₀ , E[{right arrowover (x)} ₀ {right arrow over (x)} ₀ ^(T) ]=P ₀ , E[{right arrow over(w)} _(j) {right arrow over (v)} _(k) ^(T)]={right arrow over (0)}∀j,k  [7]P _(k) ⁻=Φ_(k-1) P _(k-1) ⁺Φ_(k-1) ^(T) +Q _(k-1)P _(k) ⁺=(I−K _(k) H _(k))P _(k) ⁻K _(k) =P _(k) ⁻ H _(k) ^(T) [H _(k) P _(k) ⁻ H _(k) ^(T) +R _(k)]⁻¹where Φ_(k) is the transition matrix.

In accordance with the present teachings, an observation matrix H_(k)and the observation (measurement) noise R_(k) are generated as follows.Assume that Δ{right arrow over (r)} and Δ{right arrow over (V)} are thefirst six Kalman filter error states defined as Δ{right arrow over(r)}=(δr_(x), δr_(y), δr_(z)) ^(T) and Δ{right arrow over (V)}=(δV_(x),δV_(y), δV_(z))^(T) in the platform coordinate frame where superscript Tdenotes the transpose of the vector. Note that if Δ{right arrow over(r)} and Δ{right arrow over (V)} are defined in the ECEF coordinateframe, then these error states need to be transformed into the platformframe where the error equations [5] are defined. The Kalman filter errorstate {right arrow over (x)}_(k), observation matrix H_(k), andmeasurement noise matrix R_(k) are denote as below:

$\begin{matrix}{{{\overset{\rightarrow}{x}}_{k} = \left( {{\delta\; r_{x}},{\delta\; r_{y}},{\delta\; r_{z}},{\delta\; V_{x}},{\delta\; V_{y}},{\delta\; V_{z}},0,\ldots\mspace{11mu},0} \right)^{T}},{H_{k} = \begin{pmatrix}{h_{00},h_{01},h_{02},h_{03},h_{04},h_{05},0,\ldots\mspace{11mu},0} \\{h_{10},h_{11},h_{12},h_{13},h_{14},h_{15},0,\ldots\mspace{11mu},0} \\{h_{20},h_{21},h_{22},h_{23},h_{24},h_{25},0,\ldots\mspace{11mu},0}\end{pmatrix}},{{{and}\mspace{14mu} R_{k}} = \begin{pmatrix}{r_{00},} & {0,} & 0 \\{0,} & {r_{11},} & 0 \\{0,} & {0,} & r_{22}\end{pmatrix}}} & \lbrack 8\rbrack\end{matrix}$Assume that the vectors {right arrow over (R)}=(R_(x), R_(y), R_(z)),V=|{right arrow over (V)}| (magnitude of {right arrow over (V)}),R=|{right arrow over (R)}|,

${\frac{\overset{\rightarrow}{V}}{V} = \left( {p_{x},p_{y},p_{z}} \right)},{{{and}\mspace{14mu}\frac{\overset{\rightarrow}{V}}{V} \times \frac{\overset{\rightarrow}{R}}{R}} = {\left( {q_{x},q_{y},q_{z}} \right).}}$Therefore, equation [5] can be expressed in the following forms:

$\begin{matrix}{{{dx}_{p} = {{\left( {p_{x} + {{R_{x} \cdot \sin}\;\phi}} \right)\delta\; r_{x}} + {\left( {p_{y} + {{R_{y} \cdot \sin}\;\phi}} \right)\delta\; r_{y}} + {\left( {p_{z} + {{R_{z} \cdot \sin}\;\phi}} \right)\delta\; r_{z}} + {\left\lbrack {\left( {p_{x} + {{R_{x} \cdot \sin}\;\phi}} \right)/V} \right\rbrack\delta\; V_{x}} + {\left\lbrack {\left( {p_{y} + {{R_{y} \cdot \sin}\;\phi}} \right)/V} \right\rbrack\delta\; V_{y}} + {\left\lbrack {\left( {p_{z} + {{R_{z} \cdot \sin}\;\phi}} \right)/V} \right\rbrack\delta\; V_{z}}}}{{dy}_{p} = {{\left( {{{R_{x} \cdot \sin}\;{\phi \cdot \cos}\;\psi} - {{q_{x} \cdot \sin}\;\psi}} \right)\delta\; r_{x}} + {\left( {{{R_{y} \cdot \sin}\;{\phi \cdot \cos}\;\psi} - {{q_{y} \cdot \sin}\;\psi}} \right)\delta\; r_{y}} + {\left( {{{R_{z} \cdot \sin}\;{\phi \cdot \cos}\;\psi} - {{q_{z} \cdot \sin}\;\psi}} \right)\delta\; r_{z}} + {\left\lbrack {\left( {{{R_{x} \cdot \sin}\;{\phi \cdot \cos}\;\psi} - {{q_{x} \cdot \sin}\;\psi}} \right)/V} \right\rbrack\delta\; V_{x}} + {\left\lbrack {\left( {{{R_{y} \cdot \sin}\;{\phi \cdot \cos}\;\psi} - {{q_{y} \cdot \sin}\;\psi}} \right)/V} \right\rbrack\delta\; V_{y}} + {\left\lbrack {\left( {{{R_{z} \cdot \sin}\;{\phi \cdot \cos}\;\psi} - {{q_{z} \cdot \sin}\;\psi}} \right)/V} \right\rbrack\delta\; V_{z}}}}{{dz}_{p} = {{\left( {{{R_{x} \cdot \sin}\;{\phi \cdot \sin}\;\psi} + {{q_{x} \cdot \cos}\;\psi}} \right)\delta\; r_{x}} + {\left( {{{R_{y} \cdot \sin}\;{\phi \cdot \sin}\;\psi} + {{q_{y} \cdot \cos}\;\psi}} \right)\delta\; r_{y}} + {\left( {{{R_{z} \cdot \sin}\;{\phi \cdot \sin}\;\psi} + {{q_{z} \cdot \cos}\;\psi}} \right)\delta\; r_{z}} + {\left\lbrack {\left( {{{R_{x} \cdot \sin}\;{\phi \cdot \sin}\;\psi} + {{q_{x} \cdot \cos}\;\psi}} \right)/V} \right\rbrack\delta\; V_{x}} + {\left\lbrack {\left( {{{R_{y} \cdot \sin}\;{\phi \cdot \sin}\;\psi} + {{q_{y} \cdot \cos}\;\psi}} \right)/V} \right\rbrack\delta\; V_{y}} + {\left\lbrack {\left( {{{R_{z} \cdot \sin}\;{\phi \cdot \sin}\;\psi} + {{q_{z} \cdot \cos}\;\psi}} \right)/V} \right\rbrack\delta\; V_{z}}}}} & \lbrack 9\rbrack\end{matrix}$Therefore, the elements in the observation matrix are as follows:h ₀₀ =p _(x) +R _(x)·sin φh ₀₁ =p _(y) +R _(y)·sin φh ₀₂ =p _(z) +R _(z)·sin φh ₀₃ =h _(00/) Vh ₀₄ =h _(01/) Vh ₁₀ =R _(x)·sin φcos ψ−q _(x)·sin ψh ₁₁ =R _(y)·sin φcos ψ−q _(y)·sin ψh ₁₂ =R _(z)·sin φcos ψ−q _(z)·sin ψh ₁₃ =h ₁₀ /V   [10]h ₁₄ =h ₁₁ /Vh ₁₅ =h ₁₂ /Vh ₂₀ =R _(x)·sin φsin ψ+q _(x)·cos ψh ₂₁ =R _(y)·sin φsin ψ+q _(y)·cos ψh ₂₂ =R _(z)·sin φsin ψ+q _(z)·cos ψh ₂₃ =h ₂₀ /Vh ₂₄ =h ₂₁ /Vh ₂₅ =h ₂₂ /Vand r₀₀, r₁₁, and r₂₂ represent the observation noise in the SAR/FLIRimager accuracy during the geo-target scan. The DTED noise is includedin r₂₂ term.

In the illustrative embodiment, the sensor position and attitude errorsare converted into the slant coordinate frame and then into the platformframe. Errors that may be due to the SAR signal processing and rangingerrors are ignored since these errors are assumed to be relativelysmall. If some of those errors are large enough to be considered, thesame method can be used to transform these errors into the platformframe and obtain similar results as equation [11] below:

$\begin{matrix}{{{dx}_{p} = {\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \left( {\frac{\overset{\rightarrow}{V}}{V} + {{\overset{\rightarrow}{R} \cdot \cos}\;\phi}} \right)}}{{dy}_{p} = {{{\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \overset{\rightarrow}{R} \cdot \sin}\;{\phi \cdot \cos}\;\psi} - {{\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \frac{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}{{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}} \cdot \sin}\;\psi}}}{{dz}_{p} = {{{\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \overset{\rightarrow}{R} \cdot \sin}\;{\phi \cdot \sin}\;\psi} + {{\left( {{\Delta\;\overset{\rightarrow}{r}} + \frac{\Delta\;\overset{\rightarrow}{V}}{V}} \right) \cdot \frac{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}{{\overset{\rightarrow}{V} \times \overset{\rightarrow}{R}}}}\cos\;\psi}}}} & \lbrack 11\rbrack\end{matrix}$

The error states in the Kalman filter should include the vehiclenavigation errors such as {right arrow over (x)}_(k)=(Δr_(x), Δr_(y),Δr_(z), ΔV_(x), ΔV_(y), ΔV_(z), . . . )^(T). The error equations abovecan be converted to an observation matrix in the Kalman filer asfollows:

$\begin{matrix}{H_{k} = \begin{pmatrix}{h_{00},} & {h_{01},} & {h_{02},} & {h_{03},} & {h_{04},} & {h_{05},} & {0,\ldots\mspace{11mu},0} \\{h_{10},} & {h_{11},} & {h_{12},} & {h_{13},} & {h_{14},} & {h_{15},} & {0,\ldots\mspace{11mu},0} \\{h_{20},} & {h_{21},} & {h_{22},} & {h_{23},} & {h_{24},} & {h_{25},} & {0,\ldots\mspace{11mu},0}\end{pmatrix}} & \lbrack 12\rbrack\end{matrix}$where h_(ij) are defined above.

In general, coordinate frames of the sensor errors and navigation errorstates in the Kalman filter are different. They need to transform intothe same coordinate frame.

The error equations in equation [1] are, in fact, a TLE in the platformcoordinate frame. Based on this invention, any TLE can be extracted andconverted into an observation matrix as described in equation [5].

If the sensor SAR/FLIR can only obtain two-dimensional images (dx_(p),dy_(p)), the observation matrix will be a two-dimensional matrix:

$\begin{matrix}{H_{k} = \begin{pmatrix}{h_{00},} & {h_{01},} & {h_{02},} & {h_{03},} & {h_{04},} & {h_{05},} & {0,\ldots\mspace{11mu},0} \\{h_{10},} & {h_{11},} & {h_{12},} & {h_{13},} & {h_{14},} & {h_{15},} & {0,\ldots\mspace{11mu},0}\end{pmatrix}} & \lbrack 13\rbrack\end{matrix}$where the elements h_(ij) are defined as before.

Thus, the present invention has been described herein with reference toa particular embodiment for a particular application. Those havingordinary skill in the art and access to the present teachings willrecognize additional modifications applications and embodiments withinthe scope thereof.

It is therefore intended by the appended claims to cover any and allsuch applications, modifications and embodiments within the scope of thepresent invention.

Accordingly,

1. A position estimation system comprising: first means for providing animage including a known target in a known reference frame; second meansfor correlating said image with a stored image; third means responsiveto said second means for computing an error in response thereto, whereinsaid error is referenced with respect to first (x), second (y) and third(z) directions; fourth means responsive to said third means forproviding an observation model; and fifth means for filtering said modelto provide a position estimate.
 2. The invention of claim 1 wherein saiderror is a target location error.
 3. The invention of claim 1 whereinsaid stored image is provided by a catalog.
 4. The invention of claim 3wherein said catalog is a target image catalog.
 5. The invention ofclaim 4 wherein said target image catalog includes target geo-locations.6. The invention of claim 5 wherein said catalog includes digitalterrain elevation data.
 7. The invention of claim 1 wherein said fifthmeans includes a Kalman filter.
 8. The invention of claim 1 furtherincluding means for providing position data and means for computing saiderror in response thereto.
 9. The invention of claim 8 wherein saidmeans for providing position data includes an inertial navigationsystem.
 10. The invention of claim 9 further including means forproviding errors with respect to a slant coordinate frame.
 11. Theinvention of claim 10 further including means for converting said errorswith respect to a slant coordinate frame to errors with respect to aplatform coordinate frame.
 12. The invention of claim 9 wherein saidmeans for providing position data further includes a Global PositioningSystem receiver.
 13. The invention of claim 1 wherein said first meansincludes a radar system.
 14. The invention of claim 13 wherein saidradar system includes a synthetic aperture radar.
 15. The invention ofclaim 1 wherein said first means includes an infrared detector.
 16. Theinvention of claim 15 wherein said first means includes aforward-looking infrared detector.
 17. The invention of claim 1 furtherincluding means for providing an observation matrix.
 18. The inventionof claim 1 further including means for providing a measurement noisematrix.
 19. The invention of claim 1 further including means for usingan observation matrix and a measurement noise matrix to correct for saiderror.
 20. A navigation system comprising: an inertial navigationsystem; a Global Positioning System receiver for minimizing an errorgenerated by said inertial navigation system; means for minimizing anerr or in position data generated by said inertial navigation system inresponse to an output from said receiver, wherein said error isreferenced with respect to first (x), second (y) and third (z)directions; means for detecting interference in reception of saidreceiver and providing a signal in response thereto; responsive to saidsignal for referencing data from target in a known location to minimizean error generated by said inertial navigation system; means responsiveto said means for minimizing for providing an observation model; andmeans for filtering said model to provide a position estimate.
 21. Aposition estimation method including the steps of: providing an imageincluding a known target in a known reference frame; correlating saidimage with a stored image; computing an error in response said step ofcorrelating said image with a stored image, wherein said error isreferenced with respect to first (x), second (y) and third (z)directions; providing an observation model in, response to said error;and filtering said model to provide a position estimate.
 22. Theinvention of claim 21 wherein said error is referenced with respect tofirst (x), second (y) and third (z) directions.
 23. The invention ofclaim 21 wherein said error is a target location error.
 24. Theinvention of claim 21 wherein said stored image is provided by acatalog.
 25. The invention of claim 24 wherein said catalog is a targetimage catalog.
 26. The invention of claim 25 wherein said target imagecatalog includes target geo-locations.
 27. The invention of claim 26wherein said catalog includes digital terrain elevation data.
 28. Theinvention of claim 21 further including the step of providing anobservation model.
 29. The invention of claim 28 further including thestep of filtering said model to provide a position estimate.
 30. Theinvention of claim 29 wherein said filtering is effected with a Kalmanfilter.
 31. The invention of claim 21 further including the step ofproviding position data and means for computing said error in responsethereto.
 32. The invention of claim 31 wherein said step of providingposition data includes the step of securing position data from aninertial navigation system.
 33. The invention of claim 32 furtherincluding the step of providing errors with respect to a slantcoordinate frame.
 34. The invention of claim 33 further including thestep of converting said errors with respect to a slant coordinate frameto errors with respect to a platform coordinate frame.
 35. The inventionof claim 32 wherein said step of providing position data furtherincludes a Global Positioning System receiver.
 36. The invention ofclaim 21 further including the step of providing an observation matrix.37. The invention of claim 21 further including the step of providing ameasurement noise matrix.
 38. The invention of claim 21 furtherincluding the step of using an observation matrix and a measurementnoise matrix to correct for said error.
 39. A navigation methodincluding the steps of: providing an inertial navigation system;providing a Global Positioning System; minimizing an error in positiondata generated by said inertial navigation system in response to anoutput from said receiver, wherein said error is referenced with respectto first (x), second (y) and third (z) directions; detectinginterference in reception of said receiver and providing a signal inresponse thereto; referencing data from a target in a known location tominimize an error generated by said inertial navigation system inresponse to said signal; providing an observation model in response tosaid error; and filtering said model to provide a position estimate. 40.A position estimation system comprising: first means for providing animage including a known target in a known reference frame; second meansfor correlating said image with a stored image; third means responsiveto said second means for computing a position estimate error in responsethereto, wherein said error is referenced with respect to first (x),second (y) and third (z) directions; fourth means for providing anobservation matrix; fifth means for providing a measurement noisematrix; and sixth means for using an observation matrix and ameasurement noise matrix to correct for said error.